To Let Someone Stay Over
To Let Someone Stay The Night
transitive verb, ichidan verb
泊まる is "to stay the night." Now you're letting someone else stay the night, which makes this to let someone stay over or to let someone stay the night.
とめる
The reading comes from 泊まる.
うちに知らない人を泊めるのは嫌です。
I don’t want to have some stranger stay at our house.